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Rewriting Formulas
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Section 1-6Rewriting Formulas
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4za. Find x when y = 2
and z = 3b. Find z when y = 2
and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w+1 +1
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
-7 = 4z
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
-7 = 4z
z = − 7
4
Question
Question
Suppose we kept working with the problem in #2. Is there a way to make the problem easier to work with if we
kept getting different values for x and y?
Solved for a variable:
Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
“in terms of”:
Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
“in terms of”: When an equation is solved for a variable, the equation is written “in terms of” the remaining variables
Example 1a. Solve for h in terms of b and A.
b =
2A
h
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
b=
2A
b
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
b=
2A
b
h =
2A
b
Example 1b. Solve for A in terms of b and h.
b =
2A
h
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
2=
2A
2
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
2=
2A
2
A = 1
2bh
Example 2Solve C = 2πr for r.
Example 2Solve C = 2πr for r.
C
2π=
2π r
2π
Example 2Solve C = 2πr for r.
C
2π=
2π r
2π
r =
C
2π
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
12
gt2 − h0+ h
−t=−v
0t
−t
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
12
gt2 − h0+ h
−t=−v
0t
−t
v
0= −
12
gt2 − h0+ h
t
Homework
Homework
p. 38 #1 - 20
